August 2019, Vol. 19, No. 4 MANUFACTURING TECHNOLOGY ISSN 1213–2489 Measuring the Performance Characteristics of a Motorcycle Adam Hamberger, Milan Daňa Regional Technological Institute, University of West Bohemia – Faculty of Mechanical Engineering, Univerzitní 8, Pilsen 306 14, Czech Republic. E-mail: [email protected] This work deals with an experiment, whose output is the comparison of power characteristics which were meas- ured in three ways. The first way used a commercially manufactured dynamometer. For the second measurement, a special dynamometer with our own computing system and a sensor within this project was created. The last way of measuring the performance characteristics was done without a dynamometer. The measurement works on the principle of acceleration the spinning of a flywheel. Due to this, the measuring is called an acceleration test. The basic principles are described before the experiment in order to grasp the characteristics. All explanations are based on schemes and easy mathematical and differential formulas to describe the construction of the dynamom- eter and the principle of its functions from the engine to the computer. The relations between published and un- published quantities defining engine dynamics are explained here. In the end, this work points to possible and intended measuring failures which are an infamous practice at many measuring stations. Keywords: Dynamometer, power characteristics, driving forces, torque, performance. Introduction These forces are divided into two basic sorts. The first one is dependent on velocity and it can be written as: All vehicle engines overcome resistances on the road. 2 Fres( v )= c21 v + c v + ( c val + sin( )) m g [ N ], (1) where: φ … climb angle [rad], v … velocity [m/s], m … full weight[kg], 2 c1,c2,croll … coefficients [-], g … gravity acceleration [m/s ]. Fig. 1 Drive force diagram and experimentally determined resistance forces on the road Most technical literature does not take the linear ele- Newton’s second law it is possible to create the equation ment into consideration. But this is a mistake, because as of vehicle acceleration: this experiment proved, it is not possible to approximate Fd()() v− F res v m the resistance equation without the linear element. This at( )= [2 ], (2) element takes into consideration viscous friction, i.e. air msred friction and friction in the chain and other components. where: The second sort of forces are inertial effects, and they are t … time [s], dependent on acceleration.[2],[8],[12] Fd … drive force [N], Before defining the known quantities, it is necessary Fres … resistance force [N], to explain what characterizes vehicle dynamics. Based on mred … reduced mass [kg], indexed on: http://www.scopus.com 573 August 2019, Vol. 19, No. 4 MANUFACTURING TECHNOLOGY ISSN 1213–2489 Because the main purpose is to analyse the engine force. As you can see in Fig.1 and Fig.2 the force curves characteristics, it is necessary to focus on the drive force. and torque curves are similar but deformed in the direc- The meaning of reduced mass will be explained below. tion of hyperbolas. Both torque curves can achieve the same force curve by means of another gear ratio. Despite Describing the characteristics this, most people would say that the engine with the red curve is stronger because its torque is higher. A typical Here are explained the basic principles of the perfor- output of a dynamometer is a graph with a power curve mance characteristics. Then the method to determine the and a torque curve. Therefore the best way to determine characteristics and resistance forces are explained in or- vehicle power is using a drive force diagram (for example der to understand the experiment in section 3. when tuning, etc.). 2.1 Drive force 2.2 Torque vs. power Drive force is the tangential force between the tyre Because it is necessary to know all the gear ratios to and the road during acceleration. This equation gives the create a drive force diagram, it is not common to publish relation between drive force and engine torque. it. The torque curve has the same course as the drive force curve. This means that the pull forward is characterized Mt() n i total Fd ( v )= [ N ], (3) by the course of the torque, not by the course of the rtyre power. This means that the torque diagram is graphical interpretation of vehicle acceleration. Despite this, the where: torque diagram is ignored in most cases. The most fre- Mt … crankshaft torque [Nm], quent question after measuring is, “How much horse- n … crankshaft revolutions [RPM], power does it have?” This is very important question but itotal … total gear ratio of vehicle [-], without the torque curve it is not so substantial. The most rtyre… drive tyre radius [m]. important fact is that the maximum torque value is totally unnecessary. The mathematical relation between torque Every gear has its gear ratio with continuous drive (Mt) and power (P) is shown in Fig.2. Fig. 2 Two engines with the same performance 2.3 Principle of measuring from the sensor is transferred to the computer. Every rev- olution of the flywheel makes a pulse and the time be- In most cases, the engine is measured using a dyna- tween the impulses is marked as dt. The full angle of mometer (abbreviated to DYNO). The main component every revolution (360°=2π rad) is marked as dφ. Now it of the dynamometer is the flywheel. The flywheel is ro- is possible to create the angular velocity for all revolu- tated by the engine power (mostly via the wheel). The tions, for example 100 values of the scanned flywheel. speed of the flywheel is monitored during measuring. These numbers are approximated by the polynomial func- Measuring is composed of two phases acceleration and – tion of degree 15 because it is easy to derivate. This pol- deceleration tests. During the acceleration test, the fly- ynomial function (t) is again derived in order to ascer- wheel is rotated with the engine torque. The operator ω opens the throttle at minimum engine speed. The flywheel tain angular acceleration α. The best way to process the is rotated to maximum engine speed and it is monitored calculated data is to create a matrix with rows for every using a revolution sensor. It is the end of acceleration test revolution. Then it is possible to change from time varia- and then the measured data are analysed in a computer. ble to RPM variable and to multiply by inertia moment in The flywheel has a scanned point (for example a mag- order to ascertain torque, etc. All these calculations are net) and the frame has a sensor (Hall sensor). The signal carried out using the reduced inertia mass method, which 574 indexed on: http://www.scopus.com August 2019, Vol. 19, No. 4 MANUFACTURING TECHNOLOGY ISSN 1213–2489 is described in [6]. Aforesaid part of measuring is called engine is separated by shifting into neutral. All masses, acceleration test. which are separated from the engine, turn by themselves The second part of measuring is the deceleration test. until they stop. This run is monitored as well as accelera- The purpose of this test is to determine the resistance tion. Both parts of the measurements are shown on the forces. After the acceleration test at the highest speed, the Fig. 3. Fig. 3 Velocity by measuring The whole data processing is done in the same way. wheel (without crankshaft), because the crankshaft is sep- So the measured torque is added to the values which were arated from the flywheel during the deceleration test. This determined in the acceleration test. This sum total can be is a simplified way to describe this process. In order to written as the engine torque and used to calculate other achieve the most accurate results, the moment of inertia values (drive force, power). This equation explains the is calculated for all moving parts using a CAD system. simplified way to determine the reduced moment of iner- Inertia calculated in this way can be approximately 80- tia when the crankshaft and dyno-flywheel spin: 98% of the inertia mass of all the moving parts. I f 2 (4) Experiment Iredtocrank= I crank +2 [ kg m ], itotal This experiment deals with determining the perfor- where: mance characteristics of the same motorcycle in three ways. The first measurement is carried out on a commer- Iredtocrank …total reduced moment of inertia to crankshaft [kg∙m2], cially available dynamometer with its own software and 2 sensors. We made our own dynamometer for the second If… moment of inertia of flywheel [kg∙m ], 2 measurement and its software was made using a graphical Icrank… moment of inertia of crankshaft [kg∙m ] user interface. The third measuring method does not need Itotal… total gear ratio between flywheel and crankshaft [kg∙m2] a dynamometer. This method is carried out on the road only by means of the system from the second measure- This value of total moment is multiplied by the angu- ment method in order to substitute the inertia of the dyno- lar acceleration of the crankshaft in order to ascertain the flywheel for the mass of the motorcycle and rider. The crankshaft torque for the acceleration itself. As already purpose of this experiment is to verify all the mentioned mentioned, for the purpose of ascertaining total torque, principles and to compare the results of all three ways of the torque of passive resistance must be added. The torque measuring. It was necessary to ascertain the inertia of all of passive resistance is scalar product of angular acceler- the moving parts. This was done using CAD models ation when deceleration test and of inertia moment of fly- which were created using reverse engineering of used motorcycle components and a dyno-flywheel.